# Thread: [SOLVED] Characterizations of a Square

1. ## [SOLVED] Characterizations of a Square

Ok, I wanted to ask the experts on this one

Im given that a square is a quadrilateral that is equilateral and equiangular.

Im asked to find 3 different characterizations of a square. I came up with the following biconditionals but dont know if there true both ways/

1.A Polygon is a square IFF it is a equilateral rectangle where every angle is a right angle.

2.Same as above Except a Parallelogram where every etc..

3.Same as above Except Rhombus

Would these be correct?

Thank you for your time and help

2. Hello, nikie1o2!

I'm given that a square is a quadrilateral that is equilateral and equiangular.

I'm asked to find 3 different characterizations of a square.
I came up with the following biconditionals but dont know if there true both ways.

1.A polygon is a square IFF it is a equilateral rectangle where every angle is a right angle.
This is a bit redundant.
"Equilateral rectangle" covers it.
(A rectangle, by defintion, has four right angles.)

2. Same as above, except a Parallelogram where every etc.
An "equilateral parallelogram with four right angles" does cover it.

3. Same as above except Rhombus
An "equiangular rhombus" covers it.
(A rhombus, by definition, is equilateral.)

I'm not sure that there are three more characteristics.

"Equilateral" already states that the sides are all equal.
"Equiangular" already states that the angles are all equal.

Are these acceptable?
. . The opposite sides are parallel (also true for a parallelogram).
. . The diagonals are equal (also true for a rectangle).
. . The diagonals are perpendicular (also true for a rhombus).
. . The diagonals bisect each other (also true for a parallelogram).